Duplicate content hurting rankings?

I have a client whom I write for. One of their blog posts (that was written a while ago by someone else) wasn't that great. I recommended sprucing it up, adding more keywords, and writing more content to match the search intent.

Last week, they published the newly written blog post.

However, their VA did something weird when publishing it and ended up creating two separate URLs for the same piece of content.

So now we have two distinct URLs with the exact same content on each page.

Google pretty much removed the original URL from the SERPs and replaced it with the new one (however, the new one isn't ranking for as many keywords, I'm assuming because it's so new and hasn't quite settled in the SERPs yet?).

As soon as I noticed, I quickly advised them to take down the duplicate, 301 redirect, fix up their sitemap, and make sure there were no internal links pointing to the duplicate.

Since the duplicate isn't ranking for as many search terms and because the original URL has pretty much dropped out of the SERPs, I'm worried that they think I'm the one who has messed up.

My question: if the client tries to blame me for writing a re-write that ruined their rankings is it fair for me to point out that this is largely a problem of duplicate content and that it's impossible to tell at this point whether it's a re-write issue or a duplicate content issue?